GCSE Maths - Reverse Percentages - Calculating The Cost Before The Discount #96

This video covers how to calculate the original value of an item after it's increased or decreased by a certain percentage. For example if a pair of sunglasses has 20% off and now costs £56, what was the original price before the discount? We often call this topic reverse percentages.

This video is suitable for maths courses around the world.
KS3 - Not on your course
GCSE Foundation - All on your course
GCSE Higher - All on your course
A-level - Basic for your course

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[Cognitoedu]

If you’d like to practise the material covered in this video, check out our platform at www.cognitoedu.org - it's totally free, and has been built to make learning and revision as easy as possible. The main features are:
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Amadeus & Tom

[noahatcha]

Wow, this channel has grown since, the beginning of 2020, I remember when it was 20k subs, well done, hard work always pays off. :)

[studyskillz]

Thank you Cognito for keeping students going through this tough time! Much love :)

[jacobbillups]

PSA for anyone who conceptualizes these problems from a different angle here is a different way to get the same answers (of course the way in the vid is completely valid this is just an alternative).
If you think of the percentages as pure decimals you can often cut a few steps. For example the first problem where the house is increased by 15% to £207, 000. Your target is the original 100%. So you can do it in one step by taking £207, 000/1.15=£180, 000.
Same method for example 2: 20% sale with new price at £72.00 (100% OG price the target again). So this time you’d take £72/0.80=£90.00.

Only one that is a tad counterintuitive is the one where you are given the % and the change in price but neither original nor new total. In that case you take that price change (delta) and divide it by the % given in decimal form (sounds complex but really easy in practice). So for the example problem 5% increase=£42.50.
Take £42.50/0.05=£850. Then finally since 850 is the OG price you’d add that £42.50 on top for the £892.50 new price. Lastly to drive the point home let’s say that problem was the same but it was a decrease/discount instead. Everything would be the same save the last step where you’d subtract the 42.5 from 850 in the end.

Side note with any problem like this it’s easy to accidentally flip things around so a good practice is to mentally check yourself as you go by asking if the number you just got makes sense. Like if you multiply the first problem by 1.15 instead of dividing it. You end up with a number higher than the 207k you started with (which makes no sense lol).

I doubt anyone will have read all that but if by some miracle you did and it helped lmk lol 😊

[sallyread]

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[pwarrow]

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[MazzBagel]

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[vihaan]

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[readerofmanga]

The first time I came across this, I managed to learn it quickly and got it right away. Realistically, I will have to revise more on this one.

[danieldavid]

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[qanatalae]

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[missesnoku]

there’s a much easier way!!! Just divide the number (207, 000) by how much the percent changed as a decimal (1.15) !! pleaseee this way is so much easier especially in calculator exams.

[ukrainianbloke]

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[WeeklyFacts-]

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[gloss]

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